Robust Matrix Completion via Novel M-Estimator Functions

As most existing M-estimators down-weigh clean observations which are not corrupted by outliers when resisting gross errors, we put forward a framework to produce numerous new robust loss functions, which only penalize outlier-contaminated entries, via combining the quadratic functions and the commonly-used M-estimators. We then apply the Welsch, Cauchy and $\ell_{p}$-norm functions to the devised framework and propose some novel M-estimators. Besides, based on the developed robust loss functions, efficient robust matrix completion algorithms with convergence guarantees are exploited. Experimental results verify the effectiveness of the proposed approaches over the competitors. Matlab codes are available at https://github.com/bestzywang.